pathaniaus wrote:The product of all the prime numbers less than 20 is closest to which of the following powers of 10?
A) 10^9
B) 10^8
C) 10^7
D) 10 ^6
E) 10^5
Find a way to do only very easy multiplication and use logical deduction on the rest.
(210 x 11 ) x (13 x 17) x 19.
To mulitply any two digit number by 11, separate the two numbers and put their sum in the middle. This easily gives
2310 x (13 x 17) x 19
Now 10 x 20 x 20 = 4000 cannot be too far from 13 x 17 and 19.
Whatever the real values are u know the 2 reamaining numbers each has 4 digits. When the smallest 4 digit number is squared you get 10^6=1 million and you know the 2 numbers above are each greater than 1000.
You can easily see that 2000 x 4000 = 8 x 10^6. 6 zero's but 8 million which is way above 1 million.
So the correct answer must be closer to 10^7
Choose C.
